Occupation Time of a Randomly Accelerated Particle on the Positive Half Axis: Results for the First Five Moments

@article{Burkhardt2017OccupationTO,
  title={Occupation Time of a Randomly Accelerated Particle on the Positive Half Axis: Results for the First Five Moments},
  author={Theodore W. Burkhardt},
  journal={Journal of Statistical Physics},
  year={2017},
  volume={169},
  pages={730-743}
}
  • T. Burkhardt
  • Published 4 August 2017
  • Mathematics
  • Journal of Statistical Physics
In the random acceleration process a point particle is accelerated by Gaussian white noise with zero mean. Although several fundamental statistical properties of the motion have been analyzed in detail, the statistics of occupation times is still not well understood. We consider the occupation or residence time $$T_+$$T+ on the positive x axis of a particle which is randomly accelerated on the unbounded x axis for a time t. The first two moments of $$T_+$$T+ were recently derived by Ouandji… 
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